Sofia Bought A Tablet That Was 15 % Off The Regular Price Of $775.If A 6% Sales Tax Was Added To The total, understanding how to calculate the final price involves a series of straightforward mathematical steps. Whether you're shopping for electronics or other items, knowing how discounts and sales tax work together can help you make informed purchasing decisions and budget effectively. In this article, we will explore the process of calculating the discounted price, applying sales tax, and understanding the importance of these calculations in everyday shopping.
Understanding the Original Price and Discount
The Regular Price of the Tablet
The original or regular price of the tablet is $775. This is the price before any discounts or taxes are applied, representing the retail price set by the seller.Calculating the Discount Amount
Sofia received a 15% discount on the original price. To find the amount she saved, we can use the formula:\[
\text{Discount Amount} = \text{Original Price} \times \frac{\text{Discount Percentage}}{100}
\]
Substituting the known values:
\[
\text{Discount Amount} = 775 \times \frac{15}{100} = 775 \times 0.15 = 116.25
\]
This means Sofia saved $116.25 on the tablet after applying the discount.
Finding the Discounted Price
Subtract the discount from the original price to find the price before tax:\[
\text{Discounted Price} = \text{Original Price} - \text{Discount Amount}
\]
\[
\text{Discounted Price} = 775 - 116.25 = 658.75
\]
So, Sofia's price after the discount but before tax is $658.75.
Applying Sales Tax to the Discounted Price
Understanding Sales Tax
Sales tax is a percentage added to the purchase price, which varies depending on the location. In Sofia's case, a 6% sales tax is added to the discounted price. This tax goes to the government and is calculated based on the price after discounts.Calculating the Sales Tax Amount
To find how much tax Sofia has to pay, use the formula:\[
\text{Sales Tax} = \text{Discounted Price} \times \frac{\text{Tax Percentage}}{100}
\]
Substituting the values:
\[
\text{Sales Tax} = 658.75 \times \frac{6}{100} = 658.75 \times 0.06 = 39.525
\]
For practical purposes, this amount is often rounded to two decimal places, resulting in:
\[
\text{Sales Tax} \approx \$39.53
\]
Calculating the Final Price Including Tax
Add the sales tax to the discounted price to determine the total amount Sofia paid:\[
\text{Final Price} = \text{Discounted Price} + \text{Sales Tax}
\]
\[
\text{Final Price} = 658.75 + 39.53 = 698.28
\]
Therefore, Sofia paid approximately $698.28 for her tablet after discounts and taxes.
Summary of the Calculation Process
Here's a quick recap of how to arrive at the final price:- Determine the discount amount: \( \$775 \times 15\% = \$116.25 \)
- Subtract the discount from the original price: \( \$775 - \$116.25 = \$658.75 \)
- Calculate the sales tax: \( \$658.75 \times 6\% = \$39.53 \)
- Add the sales tax to the discounted price: \( \$658.75 + \$39.53 = \$698.28 \)
This step-by-step process ensures an accurate calculation of the final amount paid.
The Importance of Accurate Pricing Calculations
Budgeting and Financial Planning
Understanding how discounts and taxes influence the final purchase price helps consumers budget appropriately. When shopping for big-ticket items like tablets, knowing the final cost prevents surprises at checkout.Comparing Offers and Discounts
Being able to calculate the actual savings allows shoppers to compare different deals effectively. For example, knowing that a 15% discount on a $775 item results in a savings of $116.25 helps in evaluating whether a deal is worthwhile.Business and Retail Insights
Retailers use these calculations to set competitive prices and promotional discounts. Consumers benefit from understanding these processes to make smarter purchasing choices.Additional Tips for Consumers
- Always verify the tax rate applicable in your location, as it can vary significantly between regions.
- When calculating discounts, consider using decimal approximations for easier mental math or financial software for precision.
- Remember that some items may be exempt from sales tax depending on local laws, so always check local regulations.
- Keep track of promotional discounts and their impact on the final price to maximize your savings.
